Surface plasmon resonance (SPR) sensors have become widely employed for studying biomolecular interactions. In general, SPR sensors operate according to the following principles.
At an interface between two transparent media of different refractive indices (e.g., glass and water), light coming from the side having the higher refractive index (e.g., glass) is partly reflected and partly refracted. Above a certain critical angle of incidence, θC, no light is refracted across the interface, and total internal reflection is observed. While the incident light is totally reflected under these conditions, the electromagnetic field component penetrates a short distance (e.g., tens or hundreds of nanometers) into the medium of the lower refractive index (e.g., water), creating an exponentially decaying evanescent wave. The propagation constant of the light parallel to the surface, kθ, is:
                              k          θ                =                              (                                          2                ⁢                                                                  ⁢                π                            λ                        )                    ⁢                      n            P                    ⁢                      sin            ⁡                          (              θ              )                                                          (        1        )            where: λ is the wavelength in free space, nP is the refractive index of the material having the higher refractive index (e.g., glass) through which the light impinges on the interface, and θ is the angle of incidence of the light beam.
Meanwhile, surface plasmons are evanescent surface electromagnetic waves that propagate along a metal/dielectric interface. Since these evanescent waves propagate on the boundary of an interface between a metal layer and a dielectric layer (for example, a protein layer in a water buffer), these oscillations are very sensitive to any change near the boundary, such as the adsorption of molecules onto the metal surface. The propagation constant of the surface plasmon, ksp, can be approximated as:
                              k          SP                ≈                              (                                          2                ⁢                                                                  ⁢                π                            λ                        )                    ⁢                      Re            ⁡                          [                                                                    (                                                                  e                        m                                            ⁢                                              n                        a                        2                                                              )                                                        1                    /                    2                                                                                        (                                                                  e                        m                                            +                                              n                        a                        2                                                              )                                                        1                    /                    2                                                              ]                                                          (        2        )            where em is the relative permittivity of the metal, na is the refractive index of the dielectric layer on the metal (e.g., a protein layer in a water buffer), and Re[expression] denotes the real part of the expression.
These two phenomena can be combined powerfully as follows.
If the interface between two dielectric media (e.g., glass and water) is coated with a thin layer (e.g., 50 nm) of a metal (e.g., gold), and monochromatic, p-polarized light is directed onto the interface from the side having the higher refractive index, then at a specific angle of incidence, θSP (“the resonance angle”), greater than θC, the propagation constant of the light parallel to the interface surface, kX, is equal to the real part of the propagation constant of the surface plasmon, kSP. At the resonance angle there is a resonance energy transfer between the evanescent wave and surface plasmons. This is called surface plasmon resonance (SPR). As a result of the resonance energy transfer between the evanescent wave and surface plasmons, the intensity of the reflected light at the resonance angle is sharply attenuated. If the metal layer has an appropriate thickness, then theoretically, at the resonance angle there is no reflection of the incident light.
The resonance angle may be found as the angle, θ, where k0=kX. Substituting from equations (1) and (2) above, we find that:
                                          (                                          2                ⁢                                                                  ⁢                π                            λ                        )                    ⁢                      n            P                    ⁢                      sin            ⁡                          (                              θ                SP                            )                                      =                              (                                          2                ⁢                                                                  ⁢                π                            λ                        )                    ⁢                      Re            ⁡                          [                                                                    (                                                                  e                        m                                            ⁢                                              n                        a                        2                                                              )                                                        1                    /                    2                                                                                        (                                                                  e                        m                                            +                                              n                        a                        2                                                              )                                                        1                    /                    2                                                              ]                                                          (        3        )            
It can be seen from equation (3) that the resonance angle, θSP, is dependent upon the index of refraction of the material (e.g., a biochemical material in a water solution) provided on the metal (e.g., gold) layer.
In a typical SPR biosensing experiment, one interactant in an interactant pair (i.e., a ligand or biomolecule) is immobilized on an SPR-active gold-coated glass slide which forms one wall of a thin flow-cell, and the other interactant (e.g., an analyte) in an aqueous buffer solution is induced to flow across this surface, by injecting it through this flow-cell. As the analyte binds to the ligand, for example, the accumulation of protein on the surface results in an increase in the refractive index. When light is shined through the glass slide and onto the gold surface at angles near surface plasmon resonance, the resonance angle changes very sensitively with change in the index of refraction due to the presence of biomolecules on the gold surface. This change in refractive index is measured in real time, and the result plotted as response or resonance units (RUs) versus time (a sensorgram). The extent of binding between the solution-phase interactant and the immobilized interactant can be quantified by monitoring this change in refractive index. Accordingly, SPR is capable of high sensitivity without any fluorescent or other labeling of the interactants.
In practice, a real instrument has a lateral distribution of light at the dielectric/metal interface. Furthermore, in practice the light source does not operate at just a single frequency, but has some finite bandwidth. These two factors lead to superimposed “dips” in reflectivity and a net non-zero minimum dip having a width spanning a small range of incident angles on either side of the “true resonant angle” θSP as illustrated by the reflectivity curve 10 in FIG. 1. As a result, it can be difficult to ascertain the location of the true resonance angle θSP and therefore the index of refraction of the material under test.
Algorithms have been developed for determining the minimum of the dip, corresponding to the resonance angle θSP, as a function of time during a biochemical reaction. Several such algorithms are disclosed by Knut Johansen et al., “Surface Plasm on Resonance: Instrumental Resolution using Photo Diode Arrays,” MEASUREMENT SCIENCE AND TECHNOLOGY, Vol. 11, pp. 1630-1638 (2000), which is incorporated herein by reference. Such algorithms include intensity measurements, polynomial fitting algorithms, centroid calculation algorithms, locally weighted parametric regression, and principal component regression.
However, in practice, such algorithms may produce undesirable artifacts that appear as either noise or measurement errors. As a result, the accuracy and resolution of the measurements are reduced.
What is needed, therefore, is a method of surface plasmon resonance measurement that exhibits greater sensitivity and/or lower noise. What is also needed is a surface plasmon measurement instrument that exhibits greater sensitivity and lower noise.